Problem: Simplify to lowest terms. $\dfrac{40}{45}$
Solution: What is the greatest common factor (GCD) of 40 and 45? $40 = 2\cdot2\cdot2\cdot5$ $45 = 3\cdot3\cdot5$ $\mbox{GCD}(40, 45) = 5$ $\dfrac{40}{45} = \dfrac{8 \cdot 5}{ 9\cdot 5}$ $\hphantom{\dfrac{40}{45}} = \dfrac{8}{9} \cdot \dfrac{5}{5}$ $\hphantom{\dfrac{40}{45}} = \dfrac{8}{9} \cdot 1$ $\hphantom{\dfrac{40}{45}} = \dfrac{8}{9}$